When the powertrain of a vehicle is running cold, a fuel consumption penalty is incurred overcoming the higher friction losses within the engine, transmission and differential. The investigations described in this thesis concern computational studies of a vehicle powertrain to optimize the warm-up behaviour from a cold start to achieve minimum fuel consumption by reducing the cold start penalty. The newly developed vehicle model represents a premium sector, medium sized saloon based on a Jaguar S-Type with rear wheel drive and a powertrain composed of a V6 2.71 diesel engine, a six-speed ZF 6HP26 automatic transmission and a rear differential. The formulation of a powertrain model within GT-Suite, and the use of sub-models for engine friction levels, fuel flow rates and gas-side heat transfer rates, including the effect of EGR, are described. The engine's thermal behaviour is modelled using a lumped capacity approach. A 2-mass model was adequate to describe the thermal coupling between the coolant, engine oil and the engine structure. For the gas-side heat transfer a correlation is applied that is related to a commonly used form developed by Taylor and Toong. The friction model integrated is a modified version of the Patton, Nitschke and Heywood model. The descriptions of automatic transmission and differential losses and their dependence on operating state are based on empirical maps. The model validation was based on experimental data from the testbed at the University of Nottingham, and against experimental performance data from Jaguar Cars Ltd. over the NEDC. The characteristics of heat exchangers in the coolant, oil and transmission fluid circuits have been investigated through test-bed studies. The performance of the model relative to test data illustrates the accuracy of and confidence in model predictions. Following this, the application of the model was to investigate the sensitivity and enhancement of the powertrain warm-up. First, factors influencing and improving the internal heat flows of the powertrain were investigated. Different approaches were applied to establish their effectiveness. The total fuel consumption over the NEDC was used as a measure of effectiveness. Optimisation of the internal heat flows of the powertrain through the use of a transmission cooler during the warm-up showed a positive influence on the fuel consumption. A small improvement in fuel consumption was found by using a more effective transmission cooler at a later point of the warm-up, which at the same time promoted the cabin heater performance. A vailable literature lacks the knowledge of how the coolant, engine oil, automatic transmission fluid and differential oil respond to time and magnitude of heat input. This was investigated and the information was used to develop a heating strategy for an overall powel" train improvement. The lower the heat available, the greater is the relative advantage from heating the differential oil compared to the other fluids. A clear difference was found between applying a heating strategy to a powertrain with a transmission cooler or without. The heating strategy show little sensitivity to magnitude and time and were illustrated with examples of recovered exhaust gas enthalpy and regenerative braking. For the use of a transmission cooler a clear indication is given that concentrating the heat on the differential singly or in combination is the most effective way to improve fuel economy. To heat the differential in combination the ranking for the other fluids is: engine oil, coolant and then the ATF. For a gearbox without cooling equipment the benefit of heating the gearbox oil is most favourable, followed by the differential oil and then the engine oil and coolant.

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